$f(x)$ is continuous for $\forall x \geq 0$ and monotonically decrease. $f(0)=0$. $a>0$. Is it true $$ \varlimsup_{x\rightarrow 0^+}\frac{f(x)}{x^a}=\varliminf_{x \rightarrow 0^+}\frac{f(x)}{x^a} $$ whenever both are finite or infinite?
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$\begingroup$ What is $\delta$? $\endgroup$– LSpiceCommented Apr 4, 2022 at 14:37
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$\begingroup$ The counterexample to mathoverflow.net/questions/419539/… works here, too. $\endgroup$– user473423Commented Apr 5, 2022 at 8:35
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